Question

Question: Shridhar bought two buffaloes for Rs. 30000. By selling one at a loss of 15% and the other at a gain of 19%, he found that the selling price of both buffaloes is the same. Find the cost price of each (in Rs.)
A. 10000, 20000
B.15000, 15000
C. 17500, 12500
D.16000, 14000

Answer 1

Hint: This question is based on the Profit and Loss. We know that the profit occurs when the selling Price is greater than the cost price of the product, whereas the loss occurs when the selling price is less than the cost price of the product.
Formula Used:
In order to solve this question, we have to remember these following formulas:
\[Loss\% = \dfrac{{{\rm{Loss}}}}{{{\rm{Cost}}\;{\rm{Price}}}} \times 100\]
\[Gain\% = \dfrac{{{\rm{Gain}}}}{{{\rm{Cost}}\;{\rm{Price}}}} \times 100\]


Complete step by step solution
Given:
The total price of the two buffaloes is $30000$.
Let us suppose the price of the first buffalo is $x$. Then the price of the second buffalo will be, $ = \left( {30000 - x} \right)$
The loss percentage by selling the first buffalo is,
 $15\% $
So, the selling price of the first buffalo is given as,
 $\begin{array}{c}
 = \dfrac{{\left( {100 - Loss\% } \right)}}{{100}} \times x\\
 = \dfrac{{\left( {100 - 15} \right)}}{{100}} \times x\\
 = \dfrac{{85x}}{{100}}
\end{array}$
Similarly, the gain percentage by selling the second buffalo is,
$19\% $
Then, the selling price of the second buffalo is given as,
 $\begin{array}{c}
 = \dfrac{{\left( {100 + Gain\% } \right)}}{{100}} \times \left( {30000 - x} \right)\\
 = \dfrac{{\left( {100 + 19} \right)}}{{100}} \times \left( {30000 - x} \right)\\
 = \dfrac{{119}}{{100}} \times \left( {30000 - x} \right)
\end{array}$
Now according to the question, the selling price of both buffaloes is the same, so equating both the equations we get,
$\begin{array}{c}
\dfrac{{85x}}{{100}} = \dfrac{{119}}{{100}} \times \left( {30000 - x} \right)\\
85x = 119 \times \left( {30000 - x} \right)\\
85x = 3570000 - 119x\\
204x = 3570000
\end{array}$
On further solving the above expression, we get,
$\begin{array}{c}
x = \dfrac{{3570000}}{{204}}\\
x = 17500
\end{array}$
Therefore, the cost price of the first buffalo is $x = 17500$ and, the cost price of the second buffalo is, $\begin{array}{c}
\left( {30000 - x} \right) = \left( {30000 - 17500} \right)\\
 = 12500
\end{array}$
Therefore, the correct option is (C) and the cost price is 17500 and 12500.



Note: The other way to solve this question is to take two variables say x and y representing the cost price of the first and second buffalo respectively and apply the same method as before, we would get the same answer.